Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

Limits to Redistribution and Intertemporal Wedges: Implications of Pareto Optimality with Private Information

Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

Limits to Redistribution and Intertemporal Wedges: Implications of Pareto Optimality with Private Information

Article excerpt

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Traditionally an object of interest in microeconomics, models with privately informed agents have recently been used to study numerous topics in macroeconomics.1 Characterization of Pareto-optimal allocations is an essential step in these studies, because the structure of optimal institutions of macroeconomic interest depends on the structure of optimal allocations. In models with privately informed agents, however, characterization of optimal allocations is a complicated problem, relative to models in which all relevant information is publicly available, especially in dynamic settings with heterogenous agents, which are of particular interest in macroeconomics.

The objective of this article is to characterize Pareto-optimal allocations in a simple macroeconomic environment with private information and heterogenous agents. We focus on the impact of private information on the implications of Pareto optimality. To this end, we consider two economies that are identical in all respects other than the presence of private information. In each economy, we fully characterize the set of all Pareto-optimal allocations. By comparing the structure of the sets of optimal allocations obtained in these two cases, we isolate the effect private information has on the implications of Pareto optimality.

The economic environment we consider is, on the one hand, rich enough to have features of interest in a macroeconomic analysis, and, on the other hand, simple enough to admit elementary, closed-form characterization of Pareto-optimal allocations, both with and without private information. The model we use is a stylized, two-period version of the Lucas (1978) pure capital income economy that is extended, however, to incorporate a simple form of agent heterogeneity. We assume that the population is heterogenous in its preference for early versus late consumption. In particular, we assume that a known fraction of agents are impatient, i.e., have a strong preference for consumption in the first time period, relative to the rest of the population. In the economy with private information, individual impatience is not observable to anyone but the agent. A detailed description of the environment is provided in Section 1.

In our analysis, we exploit the connection between Pareto-optimal allocations and solutions to so-called social planning problems, in which a (stand-in) social planner maximizes a weighted average of the individual utility levels of the two types of agents. These planning problems are defined and solved for both the public information economy and the private information economy in Section 2. The solutions obtained constitute all Pareto-optimal allocations in the two economies.

In the third section, we compare the Pareto optima of the two economies along two dimensions. First, we examine their welfare properties by comparing the utility levels provided to agents in the cross-section of Pareto-optimal allocations. The range of individual utility levels supported by Pareto optima in the private information economy turns out to be much smaller than that of the public information economy. In this sense, private information imposes limits to redistribution that can be attained in this economic environment. Then, we compare the structures of optimal intertemporal distortions, which are often called intertemporal wedges, across the Pareto optima of the two economies. With public information, all Pareto-optimal allocations are free of intertemporal wedges. In the economy with private information, we find Pareto-optimal allocations characterized by a positive intertemporal wedge, and others characterized by a negative intertemporal wedge. We close Section 3 with a short discussion of the implications of wedges for the consistency of Pareto-optimal allocations with market equilibrium outcomes, which are studied in many macroeconomic applications. Section 4 draws a brief conclusion. …

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